Ohio University's Surender Jain builds international relationships through the study of ring theory

April 9, 2007By Bridget Whelan

Every math problem begins with a hypothesis. When Surender Jain came to Ohio University in 1970 to found the ring theory program, he may not have predicted that he would establish the leading ring theory institution in the nation, nor a highly regarded research center worldwide. Just 31 years later, however, that's exactly what he did.

Ring theory is a form of abstract algebra that has implications for the information and communication industries. Budding technologies such as data compression, which allows you to send large jpeg or movie files through email, and cryptography, which provides the security that makes online shopping relatively safe, rely on ring theory to create a system of coding to fulfill these operations.

Non-commutative ring theory is simply a more abstract form of classical, or commutative, ring theory. It relies on the mathematical axiom that, for example, 10 divided by 2 will not yield the same result as 2 divided by 10.

Ohio University's Center for Ring Theory and its Applications, housed in three rooms on Morton Hall's fourth and fifth floors, attracts doctoral students and prominent math scholars from around the world to Athens to collaborate and lecture at the center. Since the establishment of the ring theory program, the ring theorists at Ohio University have produced 20 doctoral students, Jain said.

"We have proved our existence and our importance by our research and by our students," he said.

Jain and Ohio University ring theorists Sergio Lopez-Permouth and Dinh Huynh also have founded an algebra journal, Journal of Algebra and its Applications, published by the World Scientific Publisher, that generates funds for the center.

However, Jain adds, as the center grows in international prestige, it is steadily outgrowing its facility. Last quarter, three visiting researchers had to be housed in Alden Library because there was no space for them at the center, which is funded by the university and private donations. Visitors often make substantial donations to the center's activities as well, he says.

"They want to see the center grow," Jain explains, because the center, with its sole focus on the very specific topic of non-commutative ring theory, is a unique facility. There are other centers of algebra in the world, Jain says, but he is not aware of any center as highly specialized as the Center for Ring Theory and its Applications, which adds to its global recognition.

Math scholars worldwide, in addition the visitors who come to work at the center, want to be associated with the program, he adds. Collaborations with other prominent algebra institutions around the world have been established to accomplish this goal, including with the University of Madras in India, where the center hosted a joint conference in December.

From June 15 to 17, the center and the four ring theorists at the university's regional campuses -- Pramod Kanwar, Viet Dung Nguyen, Franco Guerriero and L. Hammoudi -- will host a similar conference at Ohio University Zanesville Campus called the "International Conference on Rings and Things."

Conferences are an important opportunity for math scholars to present new findings in their fields of research, says Jain, who notes that the Chennai conference drew mathematicians from about 10 different countries. The Zanesville conference also is expected to attract scholars from various corners of the globe.

Bridget Whelan is a writing intern with the Office of Research Communications.